Empirical work suggests that larger markets tend to increase the rate of process innovation. This is difficult to square with a standard Dixit-Stiglitz model of product variety choice. In Dixit-Stiglitz, the product space is unbounded, and an increase in product variety has no effect on firm size or elasticity of demand. A Hotelling model of product variety (where consumers and firms locate on a line, or a unit circle, describing product variety) is bounded. Desmet and Parente use such a model, and show that as market size increases (say, because population went up, or because trade was liberalized), then new firms profitably enter the market, “filling in” holes in the product circle. Because the product space becomes denser, the elasticity of demand of each consumer for any given variety falls since they now have more “similar” options. This implies the partial monopoly markup falls. With free entry of firms, zero profit is made, and in order to have zero profit with a lower markup, supply of each firm must go up. If firms sell more, then any decrease in marginal cost from increased productivity (which is purchased at a fixed cost by any firm that desires) is spread over more units. Therefore all firms will innovate more, in the sense of process innovation.
My belief is that the greatest mistake of economists post-WW2 was not endogenizing growth and innovation. Even today, you read many macro models where technology is assumed to increase exogenously. But new innovations are the source of growth, the most important process economists can understand!
https://netfiles.uiuc.edu/parente/Bigger18Sept2008.pdf (WP – final version in IER 51-2)